The world’s rising urban density expansion has resulted in a proliferation of attempts to efficiently use space and a higher level of spatial complexity in metropolitan areas. 3D geospatial data models are increasingly being embraced to facilitate communicating the spatial dimensions of complex built environments in different applications. For example, the use of 3D models in land administration systems has been recognized as a good approach for communicating the spatial complexity of legal spaces within multi‐storey buildings. The spatial extent of legal space—to which rights, restrictions and responsibilities relate in a 3D digital cadastre—needs to be accurately defined and geometrically closed; watertight. Therefore, this study aims to address the challenges regarding checking the closure of diverse 3D legal spaces and engage several techniques to formulate the watertight concept for cadastre. The research’s methodology is built on a 3D polyhedral surface using a half‐edge data structure. A primitive check is employed to assess the spatial consistency of lower‐dimensional primitives of 3D objects. Subsequently, advanced closure checks ensure the closure of volumetric legal spaces represented by 2‐manifold and non‐2‐manifold data models. The article concludes that, by adopting the proposed approaches, the internal spatial consistency of legal spaces in urban land administration will be certified.

中文翻译：

---

制定地籍不透水概念的技术进步

世界上日益增长的城市密度扩张导致有效利用空间的尝试激增，大都市区的空间复杂性也提高了。越来越多地采用3D地理空间数据模型，以促进在不同应用程序中传达复杂构建环境的空间维度。例如，在土地管理系统中使用3D模型已被认为是传达多层建筑物内合法空间的空间复杂性的一种好方法。需要对法律空间的空间范围（在3D数字地籍中与权利，限制和责任相关联）进行精确定义并在几何上封闭。防水。所以，这项研究旨在解决有关检查各种3D法律空间是否封闭的挑战，并采用多种技术来制定地籍的水密概念。这项研究的方法基于半边数据结构在3D多面体表面上构建。使用图元检查来评估3D对象的低维图元的空间一致性。随后，高级闭包检查可确保封闭由2流形和非2流形数据模型表示的合法体积空间。本文的结论是，通过采用所提出的方法，将验证城市土地管理中法律空间的内部空间一致性。使用图元检查来评估3D对象的低维图元的空间一致性。随后，高级闭包检查可确保封闭由2流形和非2流形数据模型表示的合法体积空间。本文的结论是，通过采用所提出的方法，将验证城市土地管理中法律空间的内部空间一致性。使用图元检查来评估3D对象的低维图元的空间一致性。随后，高级闭包检查可确保封闭由2流形和非2流形数据模型表示的合法体积空间。本文的结论是，通过采用所提出的方法，将验证城市土地管理中法律空间的内部空间一致性。